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September 2024 term · Mathematics for Data Science II · BSMA1003

Maths 2 End Term: 22 December 2024, Set 2 (September 2024 term)

The IIT Madras BS Mathematics for Data Science II (Maths 2) End Term paper sat on 22 Dec 2024, in the September 2024 term, set 2: 45 questions for 62 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
45
Marks
62
Duration
180 min
MCQ
15
MSQ
6
Written
24
Take as mock testPractise with answers

Updated

Official paper: IIT M IMPROVEMENT FN EXAM QDD2 22 Dec · No negative marking.

Question 1

+1 markOne correct option

THIS IS QUESTION PAPER FOR THE SUBJECT "FOUNDATION LEVEL : SEMESTER II: MATHEMATICS FOR DATA SCIENCE II (COMPUTER BASED EXAM)" ARE YOU SURE YOU HAVE TO WRITE EXAM FOR THIS SUBJECT? CROSS CHECK YOUR HALL TICKET TO CONFIRM THE SUBJECTS TO BE WRITTEN. (IF IT IS NOT THE CORRECT SUBJECT, PLS CHECK THE SECTION AT THE TOP FOR THE SUBJECTS REGISTERED BY YOU)

  1. A

    YES

  2. B

    NO

Show answer

Correct answer

  • A

    YES

Question 1 on its own page

Question 2

+2 marksOne correct option
Figure from the original question paper
  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answer

  • B
    Figure from the original question paper
Question 2 on its own page

Question 3

+3 marksOne or more correct options
Figure from the original question paper

Select all that apply.

  1. A

    Add second row to fourth row and multiply second row with −5.

  2. B

    Multiply matrix A with −5.

  3. C

    Interchange first and third row and multiply fourth row with 5.

  4. D

    Multiply second row of A with 5 and multiply third row with -1.

Show answer

Correct answers

  • A

    Add second row to fourth row and multiply second row with −5.

  • C

    Interchange first and third row and multiply fourth row with 5.

  • D

    Multiply second row of A with 5 and multiply third row with -1.

Question 3 on its own page

Question 4

+3 marksOne or more correct options
Figure from the original question paper

Select all that apply.

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answers

  • A
    Figure from the original question paper
  • B
    Figure from the original question paper
Question 4 on its own page

Question 5

+3 marksOne or more correct options
Figure from the original question paper

Select all that apply.

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answers

  • B
    Figure from the original question paper
  • D
    Figure from the original question paper
Question 5 on its own page

Question 6

+3 marksOne or more correct options
Figure from the original question paper

Select all that apply.

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answers

  • A
    Figure from the original question paper
  • B
    Figure from the original question paper
Question 6 on its own page

Question 7

+1.5 marksWritten answer
Figure from the original question paper
Figure from the original question paper
Show answer

A written answer, not marked automatically.

Question 7 on its own page

Question 8

+1.5 marksOne correct option
Figure from the original question paper
Figure from the original question paper
  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answer

  • A
    Figure from the original question paper
Question 8 on its own page

Question 9

+1 markOne correct option
Figure from the original question paper
Figure from the original question paper
  1. A

    TRUE

  2. B

    FALSE

Show answer

Correct answer

  • A

    TRUE

Question 9 on its own page

Question 10

+1 markOne correct option
Figure from the original question paper
Figure from the original question paper
  1. A

    TRUE

  2. B

    FALSE

Show answer

Correct answer

  • B

    FALSE

Question 10 on its own page

Question 11

+1 markOne correct option
Figure from the original question paper
Figure from the original question paper
  1. A

    TRUE

  2. B

    FALSE

Show answer

Correct answer

  • A

    TRUE

Question 11 on its own page

Question 12

+1 markOne correct option
Figure from the original question paper
Figure from the original question paper
  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
Show answer

Correct answer

  • A
    Figure from the original question paper
Question 12 on its own page

Question 13

+1 markWritten answer
Figure from the original question paper
Figure from the original question paper
Show answer

A written answer, not marked automatically.

Question 13 on its own page

Question 14

+1 markWritten answer
Figure from the original question paper

Find the determinant of B.

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A written answer, not marked automatically.

Question 14 on its own page

Question 15

+1 markOne correct option

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Figure from the original question paper
  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answer

  • B
    Figure from the original question paper
Question 15 on its own page

Question 16

+1 markOne correct option

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Figure from the original question paper
  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answer

  • C
    Figure from the original question paper
Question 16 on its own page

Question 17

+1 markOne correct option

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Figure from the original question paper
  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answer

  • A
    Figure from the original question paper
Question 17 on its own page

Question 18

+1 markWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Figure from the original question paper
Show answer

A written answer, not marked automatically.

Question 18 on its own page

Question 19

+2 marksWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Figure from the original question paper
Show answer

A written answer, not marked automatically.

Question 19 on its own page

Question 20

+1 markWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Figure from the original question paper
Show answer

A written answer, not marked automatically.

Question 20 on its own page

Question 21

+2 marksOne or more correct options

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Figure from the original question paper

Select all that apply.

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answers

  • A
    Figure from the original question paper
  • C
    Figure from the original question paper
  • D
    Figure from the original question paper
Question 21 on its own page

Question 22

+1 markWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Figure from the original question paper
Show answer

A written answer, not marked automatically.

Question 22 on its own page

Question 23

+1 markWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.

Find the value of a.

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Question 23 on its own page

Question 24

+1 markWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.

Find the value of b.

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Question 24 on its own page

Question 25

+1 markOne correct option

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.

How many critical points does the function f have?

  1. A

    0

  2. B

    1

  3. C

    2

  4. D

    Infinitely many

Show answer

Correct answer

  • D

    Infinitely many

Question 25 on its own page

Question 26

+2 marksOne correct option

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.

What can we conclude from the Hessian test for the function f at (0, 0)?

  1. A

    (0, 0) is not a critical point.

  2. B

    The Hessian test is inconclusive.

  3. C

    The Hessian test can be used to conclude that (0, 0) is a local maximum.

  4. D

    The Hessian test can be used to conclude that (0, 0) is a local minimum.

  5. E

    The Hessian test can be used to conclude that (0, 0) is a saddle point.

Show answer

Correct answer

  • B

    The Hessian test is inconclusive.

Question 26 on its own page

Question 27

+3 marksOne or more correct options
Figure from the original question paper
Figure from the original question paper

Select all that apply.

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answers

  • A
    Figure from the original question paper
  • C
    Figure from the original question paper
  • D
    Figure from the original question paper
Question 27 on its own page

Question 28

+1 markOne correct option
Figure from the original question paper

The transformation T is

  1. A

    bijective

  2. B

    injective but not surjective

  3. C

    surjective but not injective

  4. D

    neither injective nor surjective

Show answer

Correct answer

  • B

    injective but not surjective

Question 28 on its own page

Question 29

+1.5 marksWritten answer
Figure from the original question paper
Figure from the original question paper
Show answer

A written answer, not marked automatically.

Question 29 on its own page

Question 30

+1.5 marksWritten answer
Figure from the original question paper
Figure from the original question paper
Show answer

A written answer, not marked automatically.

Question 30 on its own page

Question 31

+1 markWritten answer
Figure from the original question paper
Figure from the original question paper
Show answer

A written answer, not marked automatically.

Question 31 on its own page

Question 32

+1 markOne correct option

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Figure from the original question paper
  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answer

  • B
    Figure from the original question paper
Question 32 on its own page

Question 33

+2 marksWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Figure from the original question paper
Show answer

A written answer, not marked automatically.

Question 33 on its own page

Question 34

+1 markOne correct option

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Figure from the original question paper
  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answer

  • D
    Figure from the original question paper
Question 34 on its own page

Question 35

+1 markWritten answer
Figure from the original question paper
Show answer

A written answer, not marked automatically.

Question 35 on its own page

Question 36

+1 markWritten answer
Figure from the original question paper
Show answer

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Question 37

+1 markWritten answer
Figure from the original question paper
Show answer

A written answer, not marked automatically.

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Question 38

+1 markWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Show answer

A written answer, not marked automatically.

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Question 39

+1 markWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Show answer

A written answer, not marked automatically.

Question 39 on its own page

Question 40

+1 markWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Show answer

A written answer, not marked automatically.

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Question 41

+1 markWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Show answer

A written answer, not marked automatically.

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Question 42

+1 markWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Show answer

A written answer, not marked automatically.

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Question 43

+1 markWritten answer
Figure from the original question paper
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Question 44

+1 markWritten answer
Figure from the original question paper
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Question 45

+1 markWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
Show answer

A written answer, not marked automatically.

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